How to remove a photo from an album on my iPhone 14 without deleting it from iCloud?

Here's the thing:  In Photos, pictures aren't exactly "in" an album. When you "put a picture into an album," its name is added to a list of pictures from the Library that display together when the album is clicked, kind of like a music playlist, but for pictures. So two albums can both have the same picture name in their lists (like two playlists with the same song,)  and that picture will show up when you click either album, but there's only one picture file-- it's just on multiple lists.

So, when you remove a picture from an album, its name remains in the lists of other albums, and the file still remains in your Library. So, when asked, choose "Remove from Album," not "Delete from Library."

You don't get fewer pictures in your Library because you remove one from an album; you just get fewer names in the album list. And since albums are just lists of pictures from the Library, if you remove a picture from the Library, then they are removed everywhere.

You bet--happy photosing!